What would be the appearance of the Moso ruo,k .v6s4ap(-kuon if it had
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to have burned the wholn97afsfh2bjn -w6t 7qete x6/e Roman fleet in the harbor of Syracuse by focusing the rays of the t69-/tefesah7 fw j7 bnnx62qSun with a huge spherical mirror. Is this reasonable?

Although a plane mirror appears to reverse left and right, it doezkivx7n ko7rzf 9+43ujt ,,, qjv-yywsn’t reverse up and div-ywvkk,4z7 , n,zr 3fqx9uoyj7 +tjown. Explain.

If a concave mirror produces a real image, is the image necessarily inverted? Ej z+uy2tua.c3xplaintj. ac+23 uuzy.

An object is placed along the princn9fdu5j-pu vm0 j8n(y : dx,,h,bcw gcipal axis of a spherical mirror. The magnification of the object is -3u v8 ,:h nm 0p-,gduwcb,f(9dx 5jjcyn.0 Is the image real or virtual, inverted or upright? Is the mirror concave or convex? On which side of the mirror is the image located?

Using the rules for the three rays discussed with reference to (Fig. Below a), dk5o)2gv9i(dkcw,gg; s i vp5rraw ray 2 fok(95gii,)g ws v cd2;krgop5vr (Fig. Below b).
(a)
(b)

What is the focal length of a plane mirror? u1 gh6 33oszvzWhat is the magnification of a plane m3v631 zsgh zuoirror?

When you look at the Moon’s reflection from a ripplqr.drc1-zb q .y sea, it appears elongated . Expqrd-qcrz. . b1lain.

What is the angle of nxot5vq ;v1 ,pgiea+ d l(/9mirefraction when a light ray meets the boundary between two materials perp, o+d apv1g5lq(9vnx/ ei;imtendicularly?

How might you determine the: kdj iqzc7vj4;zpa/; speed of light in a solid, rectangular, transparent object? qda;ic7;zk p4j /zv:j

When you look down into a swimming pool or a lake, are you 1x6:ht6 daq bdc54bw f oa81yslikely to underestimate or overestimate itwd6a 45 bqb1shyf6d c8x: oat1s depth? Explain. How does the apparent depth vary with the viewing angle? (Use ray diagrams.)

Draw a ray diagram to show why a stick ly, .;.deewwdc e/t952b rjl5k e5hpup ooks bent when part of it is under water (Fig d. p.hptukdy ,rbj9e ;55c25we/ wlee. Below).

Your eye looks into an aquarium and vid8rb6d2 8u;, m0k srbel 80y*ejajrhsews a fish inside. One ray of light that emerges from the tank is shown in (Fig. Below), as well as the apparent position of*eh6b l er8m28d adj,08bsuy0rjk ;rs the fish. In the drawing, indicate the approximate position of the actual fish. Briefly justify your answer.

How can you “see” a round drop of water on a tkn9 u10yw)wkq vc7ik;rdq.l, able even though the water is transpare qw7k,k k1u9lqncd) vywr .;i0nt and colorless?

When you look up at an object in air from beneathm-tq g(va d9x4 the surface in a swimming pool, does the object appear to gaxqd(m 4-9v tbe the same size as when you see it directly in air? Explain.

How can a spherical mirror have nncd/.m/)mc-w5 rputa.la1v a negative object distance?

Light rays from stars (including our Sun) always bend toward the vertical direc zf*cfzf0it v9:nc f43tion as they pass throu 94*fvfff :i3z0c tcnzgh the Earth’s atmosphere.
(a) Why does this make sense?
(b) What can you conclude about the apparent positions of stars as viewed from Earth?

Where must the film be placed if a camera lens is to ( .avaho:/oph h)q :llfjf6/bmake a sharp image of an object vf.f ol)h/:l6jp/ov( : bahqha ery far away?

What type of mirror is shown in (Fig. mjpz1 tpu04(p-bbj q,go3r i+Below)? Explain.

A photographer moves closer to his subject and then n7vio;;e8x gaclq;1n refocuses. Does the camera lens move farther from or closer to the fi1aqn c ex;7;i;gnv lo8lm? Explain.

Can a diverging lens form a real image under any circumsp q lbdoc:cwn h;38ur i5.55kqtances? Explain.

Use ray diagrams to show that a real zk.j4myz5j22go r.qp image formed by a thin lens is always inverted, whereas a virtual image is always upright if the object is r .r22.pqgyo jmjz5k 4zeal.

Light rays are said u8u9ep4qaxo8b: -nsk/x k1wi/:yzbwto be “reversible.” Is this consistent with the thin lens equationz1:u/ix8p:4owk u-qksb aye n 8w9b/x? Explain.

Can real images be projected on a screen? Can virtuatw5m,nn qx6 zl /q7k3tl images? Can either be photographed?, 3 kn7nwzt lt5/qmq6x Discuss carefully.

A thin converging lens is moved closer to a nearby oqc7fq1+11e n wmmmy- ebject. Does the real image form 1qnemc1y 7feq1wm-m+ed change
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a material with an index lzsgto(v ow93 ) /i6umof refraction n = 1.30 In air, it is a converging lens. Will it still be a con/6(l)93iwvo ugmts ozverging lens if placed in water? ----待选择----yesno  Explain, using a ray diagram.

  A dog with its tail in the air stands facing a converging lens. If the nose36.ptbh2e4jsymxv*-u, : m apyjdxi5 and the tail are each focused ouppv3dxby* m sat6em54,2jij -hx.y: n a screen in turn, which will have the greater magnification? ----待选择----nosetail 

A cat with its tail in the air stands fvy1-os),0(t r lwa/s; sxftzsacing a converging lens. Under what circumstances (if any) would vzas1 f;ts)s-,x (srt lwy0/othe image of the nose be virtual and the image of the tail be real? Where would the image of the rest of the cat be?

Why, in Example 13, mu9+ bbes 5x-hzgn7.m oest the converging lens have a shorter focal length than the diverging lens if the latter’s focal length is to be determined by combinies7o9m+ bg5e zbn.- hxng them?

Explain how you could hqync 3* b5rabx7:3w wgave a virtual object.

  An unsymmetrical lens (say, planoconvex) forms an image of a nearby object. Doe-w w0bws/b oxo*isl 1f /uubkq8:a1o0s the image point chanbq /f10 xk-bs/0w uiw8uw1lo:ba*soo ge if the lens is turned around? ----待选择----yesno 

The thicker a double convex lens is in tdztlkc9y(,qgd u 9nk- imi5(ql w)s;4he center as compared to its edges, the shorter its focal length for a gii( il5d)u,9gyk4 c m9; k lzt-qnwsqd(ven lens diameter. Explain.

Consider two converging lenses separateccv1*svi0i jmpp5u4u+a.k/l d by some distance. An object is placed so that the image from the first lens lies exactly +*u. sivj m40vup1pl a/ ci5ckat the focal point of the second lens. Will this combination produce an image? If so, where? If not, why not?

  Suppose that you want to take a photograph of yourself aoq8 kw;us -.crxki9uzu j*0 )ys you look at your image in a flat mirror 2.5 m awu *x 9wuz8curyk-o.i s0kj)q;ay. For what distance should the camera lens be focused?    m

When you look at yourself in a 60-cm-tall plane mirror, you slpodi+b -83agvb2wl 2 ee the same amount of your body whether you are close to the mirror or far away. (Try it and see.) Use ra23 oi8gpd2vbb+w-lal y diagrams to show why this should be true.

  Two mirrors meet at a 135bmf+i xqbk fz 9;87(yt$^{\circ}\,$ angle, (Fig. Below). If light rays strike one mirror at 40$^{\circ}\,$ as shown, at what angle $\phi$ do they leave the second mirror?    $^{\circ}\,$

  A person whose eyes are 1.68 m above the floor stands 2.20 m in front of a v/*t8u 3svjv cg 3mpoz0ertical plane mirror whose bottom edge is 43 cm above the floor, (Fig. Below). What is the horizontal distance x to the base of the wall supporting the mirror of gvp ojzc*m3s3tuv8/0 the nearest point on the floor that can be seen reflected in the mirror?    cm

  Suppose you are 90 cm from a plane mirror. What areo v5t rh2jn)j/-.hs rfa of the mirror is used to reflect the rays entering one eye from a point on th. r52rvfn-jh/j to)h se tip of your nose if your pupil diameter is 5.5 mm?   $\times10^{-6}\,m^2$

Show that if two planeo ;zg .8xqll4q mirrors meet at an angle $\phi$. a single ray reflected successively from both mirrors is deflected through an angle of $2\phi$ independent of the incident angle. Assume $\phi<90^{\circ}$ and that only two reflections, one from each mirror, take place.

  A solar cooker, really a concave mirror pointed at the Sun, focuses the Sun’s rayvb5vt(b-ftyow* ya6ki xro;o:/ 0 b.ys 18.0 cm in front of the mirror. What is the radius * wy:tyob vy0bibxk 6f. or5a/(v-t ;oof the spherical surface from which the mirror was made?    cm

  How far from a concave mirror (radius 23.0 -esx7i35 adep cm) must an object be placed if its image iss73 dxiea 5e-p to be at infinity?    cm

  If you look at yourself in a shiny Christmas tree ball with a diameter of pzi :.lqhejw1wjwid 89gf-u/ ( ogk1 49.0 cm when your face is 30.0 cm away from it, where is your image? Is it rej-1g /gwudl(k.wqeiho p 9jfwz841: i al or virtual? Is it upright or inverted?
   cm behind the surface, virtual
 ----待选择----invertedupright 

  A mirror at an amusement park shows an upright ima0el 9 z*jjplra,42e jln /8wvoy +iao*ge of any person who stands 1.4 m in front of it. If the image is three times the person’s height, what is the radius ofy2a,8ljlw jpj+v e4r /0oo9en*azi*l curvature?    cm

  A dentist wants a small mirror that, when 2.20 cmsye *a)+:j lx)6kaitmy6ouk0 from a tooth, will produce a $\text{4.5×upright}$ image. What kind of mirror must be used and what must its radius of curvature be?
 ----待选择----convexconcave 
r =    m

  Some rearview mirrors produce images of b:hlhn-xgu .)cars behind you that are smaller than they would be if the mirror were flat. Are the mirrors concave or convex? What is a mirror’s radius of curvature if cars 20.0 m away ):xun-gl h.hb appear 0.33× their normal size?
 ----待选择----convexconcave 
r =    m

  A luminous object 3.0 mm hig wlxpx 0pj* 6u3q fx7l,orf-i5h is placed 20.0 cm from a convex mirror of radius of curvatruf*x6x7o3,jp f-l wl0q5xi pure 20.0 cm.
(a) Show by ray tracing that the image is virtual, and estimate the image distance.    cm
(b) Show that the (negative) image distance can be computed from Eq. 23–2 using a focal length of -10.0cm
(c) Compute the image size, using Eq. 23–3.    mm

  You are standing 3.0 m from a convex security mirror in a store. You estimate o5lc8m kz*xa*the height of your image to be half of your actual height. Estimate the radius of curvature of the mirr5*a xl*o k8zcmor.    m

  (a) Where should an object be placed in f ptyr y2l0z.a 1cs puhe2l*n p8d4,h,xront of a concave mirror so that it produces an image at the same loca2hey.p p d ytu,2xa,c znp0lrs*l 18h4tion as the object?
(b) Is the image real or virtual?  ----待选择----realvirtual 
(c) Is the image inverted or upright?  ----待选择----invertedupright 
(d) What is the magnification of the image?   

  The image of a distant tree is virtual and r :xh-1 qrvxa1efqfjd3q *u6g+(zf z0very small when viewed in a curved mirror. The image appears to be 18.0 cm behind the mirror. What kind of mirror isq1qxfef:q3+rz u - rag* fj(1d0x 6zvh it, and what is its radius of curvature?
 ----待选择----convexconcave 
r =    cm

Use two different techniqv :fuj *-)lhimyp7i ;gues,
(a) a ray diagram,
(b) the mirror equation, to show that the magnitude of the magnification of a concave mirror is less than 1 if the object is beyond the center of curvature $C\left(d_0>r\right),$ and is greater than 1 if the object is within $ C (d_0 < r) $.

Show, using a ray diagram, that the xg2ool 3b8/ sr 7z2ndiugkd. 9kw -7fymagnification m of a convex mirror is $m=-d_\mathrm{i}/d_\mathrm{o},$ just as for a concave mirror. [Hint: consider a ray from the top of the object that reflects at the center of the mirror.]

Use ray diagrams to show that the mirror equation, Eq. 23–2, is valy x14o-,u +dob0qxsce ) gx:dgid for a convex mirror as long as f is con)yx s :ggu1ed 4o,+xdoqb0xc-sidered negative.

  The magnification of a convex mir)9wq:q eyia3* v(qgmbkxu 9q+ror is $+0.65\times$ for objects 2.2 m from the mirror. What is the focal length of this mirror? $\theta_2$ =    $^{\circ}\,$

  A 4.5-cm-tall object is placed 28 cm in front of a spherical mirror.)he3s lbo 4u(b It is desired to produce a virtual image thatbbs4u(l) eho3 is upright and 3.5 cm tall.
(a) What type of mirror should be used?  ----待选择----convex mirrorconcave mirror 
(b) Where is the image located?    cm behind the surface
(c) What is the focal length of the mirror? $f$ =    cm
(d) What is the radius of curvature of the mirror? r =    cm

  A shaving/makeup mirror ix5n 8 pn5h3ukes designed to magnify your face by a factor of 1.33 when your face hp85uk3exn5 nis placed 20.0 cm in front of it.
(a) What type of mirror is it?  ----待选择----convex mirrorconcave mirror 
(b) Describe the type of image that it makes of your face.
(c) Calculate the required radius of curvature for the mirror. r =    cm

  What is the speed of light 0s.mlaw1br4gc g 1j3win
(a) crown glass,    $ \times10^{8 }\;m/s$
(b) Lucite,    $ \times10^{8 }\;m/s$
(c) ethyl alcohol?    $ \times10^{8 }\;m/s$

  The speed of light ifdalpo2y(mx 2 w0sw *5n ice is $2.29\times10^8\mathrm{~m/s}.$ What is the index of refraction of ice? n =   

  The speed of light in a certain substance is 89% of : *i28sazsknh)2poilits value in water. What is the index of refr *: z2pis8nsoihkl)a 2action of this substance? n =   

  A flashlight beam strikes the surface o.g,ndffwaxm 8 /i+9 7n.orkkpf a pane of glass (n = 1.58) at a 63$^{\circ}\,$ angle to the normal. What is the angle of refraction? $\theta_2$ =    $^{\circ}\,$

  A diver shines a flax9/txy 8n 6o4gws-i vbshlight upward from beneath the water at a 42.5$^{\circ}\,$ angle to the vertical. At what angle does the light leave the water? $\theta_2$ =    $^{\circ}\,$

  A light beam coming from an uipo o95;ji/+sd ov3 minderwater spotlight exits the water at an angle of 66.0j3o95sdioiimv ; po/+ $^{\circ}\,$ to the vertical. At what angle of incidence does it hit the air–water interface from below the surface? $\theta_1$ =    $^{\circ}\,$

  Rays of the Sun are seen to make .l2d+2 ewn8svsnt v4d z gry)7a 31.0$^{\circ}\,$ angle to the vertical beneath the water. At what angle above the horizon is the Sun?    $^{\circ}\,$

  An aquarium filled with water has0m*lq j4y,d wyhypea348v-pr flat glass sides whose index of refraction is 1.52. A beam of light from outside the aquarium strikes the glass at a 43.5° angle to the perpendicular (Fimlv40j*84q-pe pd yhy 3wry ,ag. Below). What is the angle of this light ray when it enters
(a) the glass, $\theta_2$ =    $^{\circ}\,$
(b) the water? $\theta_3$ =    $^{\circ}\,$
(c) What would be the refracted angle if the ray entered the water directly? $\theta_3'$ =    $^{\circ}\,$

  In searching the bottom of a pool at night, a watchman shines a narrow beam6,g fgaoh 68so * hkg7)qokv)c of light from his flashlight, 1.3 m kh7a , fqg66g h8o cv*))ksgooabove the water level, onto the surface of the water at a point 2.7 m from the edge of the pool (Fig. Below). Where does the spot of light hit the bottom of the pool, measured from the wall beneath his foot, if the pool is 2.1 m deep?    m

  Light is incident on an equilateral glas9mrrsty47i0c s prism at a 45.0$^{\circ}\,$ angle to one face, (Fig. Below). Calculate the angle at which light emerges from the opposite face. Assume that n = 1.58.    $^{\circ}\,$ from the normal

  A beam of light in air strikes a slab of glass (n f 9j2l4 vft2:fk fscc t-f;w-g= 1.52) and is partially reflected and partially refracted. Find the angle of incidence if the angle of reflection is twice the angle otljfcg2s :24f--vkt9ffwfc ;f refraction.    $^{\circ}\,$

Prove in general that ujsgu-h0 a .5wfor a light beam incident on a uniform layer of transparent material, as in (Fig. Belowjua -sh50 wu.g), the direction of the emerging beam is parallel to the incident beam, independent of the incident angle $\theta$. Assume air on both sides of the glass.

A light ray is incident on a)1v0 x;0yv-l:p ylnow8c ba ou flat piece of glass with index of refraction n as in (Fig. Belo0)lu xoacnv 1yv 0;8o:b-plyw w). Show that if the incident angle $\theta$ is small, the emerging ray is displaced a distance $d=t\theta(n-1)/n$ from the incident ray, where t is the thickness of the glass and $\theta$ is in radians. [Hint: for small $\theta,\sin\theta\approx\tan\theta\approx\theta$ in radians.]

  What is the critical )8)yssa k kmp nyn2cuhx7w 433angle for the interface between water and Lucite? To be totally internally reflectedu )ms2wh3k x 4)cn8sp7ky3n ya, the light must start in which material?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle for a certain liquid–air surfac*ic(n m p57gice is 47.7$^{\circ}\,$. What is the index of refraction of the liquid? $n_{liquid}$ =   

  A beam of light is emitted in a pool ofctvahmzc 8/k8 snw/.4 m mvp2( water from a depth of 62.0 cm. Where must it strike zn/whp m 8am(k4c/t28 vm sc.vthe air–water interface, relative to the spot directly above it, in order that the light does not exit the water?    cm

  A beam of light is emitted 8.0 cm beneath the surface of a liquid ira4nm r:)3 p3xofvjd 45 -jkaand strikes the surface 7.0 cm from the point directly above the source. If total internal reflection occurs, what can you say about the i 3f4a4p)jdm5r vkai3-oj: nrxndex of refraction of the liquid? $n_{liquid} \geq$   

  Suppose a ray strikes the leftmvaz1+m xwepq-m/ 6q7 a)hbb 3 face of the prism in (Fig. Below) at 45.0$^{\circ}\,$ as shown, but is totally internally reflected at the opposite side. If the prism apex angle (at the top) is $\phi=75.0^\circ,$ what can you say about the index of refraction of the prism? $n \geq$    (retain three decimal places)

A beam of light enters the end of an optic fiber as shown in (Fig. Below). Show i fah:.ts, l 2ubh42mkthat we can guarantee total internal reflection at the side surface of the material (at point a), if the index of refraction is greater than about 1.42.uhi.al2 2bm4 h,k sf:t In other words, regardless of the angle the light beam reflects back into the material at point a.

  (a) What is the minimum index of refraction for a glass or plastic pri l*z+:vz*gxg7oa cy :vsm to be used in binoculars (Fig+zcg7*:l*: o v ayvgzx. Below) so that total internal reflection occurs at 45$^{\circ}\,$? $n_1$ $\geq$   
(b) Will binoculars work if its prisms (assume n=1.50) are immersed in water?  ----待选择----totally reflectingtotally transmitting 
(c) What minimum n is needed if the prisms are immersed in water? $n_1$ $\geq$   

  A sharp image is located 78.0 mm behind a 65.0-mm-i 7sli7 6 1jcd:xkcw3fh.fjz+ focal-length converging lens. Find the ozsix3c1hd.jf l f6jw7ki7+ c:bject distance
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to focus at a 2 d2g(iqsskx.+rg28zs 0 zo utpoint 18.5 cm behind a lens.
(a) What kind of lens is it?  ----待选择----converging lensdiverging lens 
(b) What is its power in diopters? P =    D

  A certain lens focuses light from an object 2.75 m aax(pkx t5rf8hmi ( u1a5lql/k; lf /9mway as an image 48.3 cm on the other side of the lens. What type of lens is it and what is its focal lli / mf/a8(q5mh( 5trxpk 1lakf9x;lu ength? Is the image real or virtual?  ----待选择----converging lensdiverging lens  $f$ =    cm the image is  ----待选择----realvirtual 

  (a) What is the power of a 20.5-cm-focal-length lens+; 6lw/ncu u7q)pfalk m*enb +? P =    D  ----待选择----converging diverging 
(b) What is the focal length of a lens? $f$ =    cm  ----待选择----converging diverging 
(c) Are these lenses converging or diverging?

  A stamp collector uses a converging lens with focd9vz2z+wyz 8cal length 24 cm to view a stamp 18 cm in f z92v+zzc8ydw ront of the lens.
(a) Where is the image located?    cm behind the lens (virtual)
(b) What is the magnification? m =   

  A -5.5-D lens is held 14.0 cm from an object 4.0 mm hig.l b uz a0me7wjqpc9(jx 1v8j2h. What are the position, typc.0p 8z1mujw vxjeqbj2( a97 le, and height of the image?
   cm (virtual image behind the lens)
$h_1$    mm (upraight)

  An 80-mm-focal-length lens is use.n 0amg 2mhua/d to focus an image on the film of a camera. Th/ ga. amu20nhme maximum distance allowed between the lens and the film plane is 120 mm.
(a) How far ahead of the film should the lens be if the object to be photographed is 10.0 m away?    mm
(b) 3.0 m away?    mm
(c) 1.0 m away?    mm
(d) What is the closest object this lens could photograph sharply?    mm

  It is desired to magnify reading material by a factor of 2.5× when a 5+v k;zrut h9: )b qaht20s h-fokt(rmbook is placed 8.0 cm bek5t )s-h hb(t qf2vk;ru:zhoam 0 t+9rhind a lens.
(a) Draw a ray diagram and describe the type of image this would be.  ----待选择----realvirtual 
(b) What type of lens is needed?  ----待选择----converging lensdiverging lens 
(c) What is the power of the lens in diopters? P =    D

  An object is located 1.5 m from an 8.0-D lens. By how much does thelc 42;0wgt0yjzwi ,kh image move if the object is moved gztj hw;2 l0wyk 4ci0,
(a) 1.0 m closer to the lens,    cm away from the lens
(b) 1.0 m farther from the lens?    cm cm toward the lens

  How far from a converging lensv:oxfe d8hr xqgf.a g 3fhq(i4i *h7+, with a focal length of 25 cm should an object be placed to produce a real image which is the same sizehq38fgi*: ,i7 oehqx4h gfdx+va f(r. as the object?    cm

  (a) How far from a 50.0-mm-focal-length lens must an object bes8fwlr g ( b;)m;b0;oeec8dmq placed if its image is to be magnified 2.00× and b meerbobl; 8 8);0 fwd(qcgsm;e real?    mm
(b) What if the image is to be virtual and magnified 2.00×?    mm

  (a) How far from a 50.0-mm-fakc j/ ;2yd2xwocal-length lens must an object be placed if its image is to be magnxacd k 2;jw/2yified 2.00× and be real?    mm
(b) What if the image is to be virtual and magnified 2.00×?    mm (formed by some other piece of optics).]

  (a) A 2.00-cm-high insect is 1.20 m from kv9wwe5 k q8x nz:kz6.a 135-mm-focal-length lens. Where is the image, how hi:wvxwz 89 zq k6k.n5kegh is it, and what type is it?
$d_i$ =    mm (real,behind the lens) $h_1$ =    cm (inverted)
(b) What if $f=-135\mathrm{~mm}$?
$d_i$ =    mm (virtual,in front of the lens)
$h_1$ =    cm (upright)

  How far apart are an object and an image formed by a 75-cm-focal-length conv3uob.jmo 0nv 6vvw+ u-hvdzsz* y668jerging lens if the image is 2.5× larger than the object and is real?mud*jjo 0wbznv6 3 .s yv8uvh6v-z6o+    m

  A bright object and a viewing screen are separated by rvkg-cq( gj4m,lrywwyjy x6;//2j -oa distance of 66.0 cm. At what location(s) between the object and the scre-y/ gcljryk ,qoj4xw6 m2;jy(vrgw/- en should a lens of focal length 12.5 cm be placed in order to produce a crisp image on the screen? [Hint: first draw a diagram.] lens should be placed    cm or    cm from the object

  Two 28.0-cm-focal-length converging lenses are placed 16.5 cm apart8 jb;ui3a m (l(iala0e/4 fmfk. An object is placed 36.0 cm in front of one lens. Where will the final image formed by the seim0/ (uka e 3 alf(4;fj8albimcond lens be located? What is the total magnification?
 ----待选择----realvirtual ,
   cm beyond second lens.
m =    (inverted)

  A diverging lens wit-m7nia oidx6qg4 n-v2 g1tg(sh $f=-31.5\mathrm{~cm}$ is placed 14.0 cm behind a converging lens with $f=20.0\mathrm{~cm.}$ Where will an object at infinity be focused?  ----待选择----realvirtual ,    cm beyond second lens.

  A 31.0-cm-focal-length converging lens is 21.0 cm behind a diverging lens. Pari7rag**wvz 1zd hmy05 allel light strikes the diverging lens. After passing through the cyhgvzwi7dma*5 z r*1 0onverging lens, the light is again parallel. What is the focal length of the diverging lens? [Hint: first draw a ray diagram.]    cm

  The two converging lenses of Example 23–12 are now placed only 20.0 cm apartpk7wd.wf1/rmg42 re k. The object is still 60.0 cm in front of the first lens as in (Fig. w fg 7km12ked.wrp4/rBelow). In this case, determine
(a) the position of the final image,    cm
(b) the overall magnification.    cm
(c) Sketch the ray diagram for this system.

  Two converging lenses are placed 30.0 n;g we2ywu0ufa26sx 0 cm apart. The focal length of the lens on the right is 20.0 cm, and the focal length of the lens on the left is 15.0 cm. An object is placed to the left of the 15.0-cm-focal-length lens. A final image from both lenses is inverted and located halfway between the two lenses. How far to the left of the 15.0-cm-focal-length lens is the original sny ue gx w20;u2w0af6object?    cm

  A diverging lens with a focal length of is placed 12 cm -baeu d( 6tpe0k s0:voto the right of a converging lens with a focal length of 18 cm. An object is placed 33 cm to the left of the converging lv0 otb(ep0-:ed6us kaens.
(a) Where will the final image be located?    cm to the left of the converging lens
(b) Where will the image be if the diverging lens is 38 cm from the converging lens?    cm to the right of the diverging lens

  Two lenses, one converging with focal length 20.0 cm and one divergin;mbo( 9c/ k6:xgj ysrdg with focal length /yx rdoc6 ;m(ks b9jg: are placed 25.0 cm apart. An object is placed 60.0 cm in front of the converging lens. Determine
(a) the position    cm to the right of the diverging lens
(b) the magnification of the final image formed.   
(c) Sketch a ray diagram for this system.

A diverging lens is placed next tl./ vqxw4h l( wps7-uoo a converging lens of focal length $f_C$ as in (Fig. Below). If $f_T$ represents the focal length of the combination, show that the focal length of the diverging lens, $f_D$, is given by
$\frac{1}{f_\mathrm{D}}=\frac{1}{f_\mathrm{T}}-\frac{1}{f_\mathrm{C}}.$

  A double concave lens has surface radii of 34.2 cm and 23.8 cm.) ou g( lrn;tlaqg0; irkf15s5 What is the focal length if n = 11(s5l ogfknia;q)l 5u;trr g0.52?    cm

  Both surfaces of a double convex lens have radxyz j,.*2wj(ckl css qk6-vc+ ii of 31.0 cm. If the focal length is 28.9 cm, what is the x,zcsk-qwjy 2lck.v(*s+ cj6 index of refraction of the lens material?    cm

  A planoconcave lens (n=1. 8tb.u hpn3 hv9zibdw3-ls47 f50) has a focal length of -23.4cm. What is the radius of the c8z9sd uw- pfhibbt.hn7v3l 34 oncave surface?    cm

  A Lucite planoconcave lens (see Fig. Below) has one flat surface and the oth e+m:b 5vubo(ler has R = -18.4 cm. What is the focalbu:5l +vboem ( length?    cm

  A symmetric double convex lens with a focal length of 25.0 cm is to e0/ zcj/3w sq (2rx be/i5jtvjbe made from glass with an index of refraction of 1 jv sc/ zq/(ejr 3/2bjiw0t5ex.52. What should be the radius of curvature for each surface?    cm

  A prescription for a :8 sz( erednk1nzb1z- .czuh(corrective lens calls for +1.50D. The lensmaker grinds the lens from a “blank” with n=1.56 and a preformed convex front surface of radiusc- rz:b1u(hen enzd .8zk 1sz( of curvature of 40.0 cm. What should be the radius of curvature of the other surface?    m (convex)

  Two plane mirrors face each other 2.0 m apart as in (Fig. Bkopwwho k5xpe ;1v/:im6 7 kr7elow). You stand 1.5 m away from one of these mirrors and look ik 5mpr k o;6/7okwpv1wi:h7e xnto it. You will see multiple images of yourself.
(a) How far away from you are the first three images in the mirror in front of you?
$d_1$ =    m
$d_2$ =    m
$d_3$ =    m
(b) Are these first three images facing toward you or away from you?
the first image is facing  ----待选择----toward youaway from you ;
the second image is facing  ----待选择----toward youaway from you ;
the third image is facing  ----待选择----toward youaway from you .

  We wish to determine the depth o 1+alawv2sqhm)2 +x::hdj a/i 7 jplvkf a swimming pool filled with water. We measure the width (x=5.50m) and then note that the botto2h wa1 pvxl: v+kaa2jqs) +7l m/dih:jm edge of the pool is just visible at an angle of 14.0$^{\circ}\,$ above the horizontal as shown in (Fig. Below). Calculate the depth of the pool.    m

  The critical angle of a certain piecwra9(.dx u-(zwh+qvfyw km;74eim v / e of plastic in air is $\theta_{\mathrm{C}}=37.3^\circ.$ What is the critical angle of the same plastic if it is immersed in water?    $^{\circ}\,$

(a) A plane mirror can be considf avc,/ +6tlb:fn fx/y 4gpkl3ered a limiting case of a spherical mirror. Specify whac4knff/gbxl6yfp3 l v ,a/+:tt this limit is.
(b) Determine an equation that relates the image and object distances in this limit of a plane mirror.
(c) Determine the magnification of a plane mirror in this same limit.
(d) Are your results in parts (b) and (c) consistent with the discussion of Section 23–2 on plane mirrors?

Stand up two plane mirrors so they form a 90j /l7w -21 ag9q7gexett/ry f:qyi;dx$^{\circ}\,$ angle as in (Fig. Below). When you look into this double mirror, you see yourself as others see you, instead of reversed as in a single mirror. Make a careful ray diagram to show how this occurs.

Show analytically that a diverging lens can nexh0(xd9vkpo as7 +)+ee6cf zgver form a real image of a real object.oe+cdvgx)fkz9 e6(s 0 h+xap7 Can you describe a situation in which a diverging lens can form a real image?

  Each student in a physics lab is assigned to find the location where a bright o/; gatbz r4u,tbject may be placed in order that a concave mirror with radius of curvature r = 40 cm will produce an image three times the size of the object. Two students complete the assignment at different times using identical equipment, but when they compare notes later, they discover that their answers for the object distance are not the same. Explain why they do not necessarily need t4 g t,rb;a/ztuo repeat the lab, and justify your response with a calculation.
$d_o$ =    cm    cm

  If the apex angle of a prism is2 g -(btzdp:mhnpc6b* p +t(rx $\phi=72^\circ$ see (Fig. Below), what is the minimum incident angle for a ray if it is to emerge from the opposite side (i.e., not be totally internally reflected), given $\mathrm{n=1.50~?}$ $\theta_1$$\geq$    $^{\circ}\,$

The end faces of a cylindrical ocd k;:zq9rd, 2g mge6glass rod $(n=1.54)$ are perpendicular to the sides. Show that a light ray entering an end face at any angle will be totally internally reflected inside the rod when the ray strikes the sides. Assume the rod is in air. What if it were in water?

A lighted candle is placed 33 cm in front of a converging lens of 0(cj2u+ksu byfocal length $f_1=15\mathrm{~cm},$ which in turn is 55 cm in front of another converging lens of focal length $f_1=15\mathrm{~cm},$ (see Fig. Below).
(a) Draw a ray diagram and estimate the location and the relative size of the final image.
(b) Calculate the position and relative size of the final image.

A bright object is placed ongh6m b,2ghro. one side of a converging lens of focal length f, and a whgg6hm.bo r,h2 ite screen for viewing the image is on the opposite side. The distance $d_T=d_i+d_o$ between the object and the screen is kept fixed, but the lens can be moved.
(a) Show that if $d_{\mathrm{T}}>4f,$ there will be two positions where the lens can be placed and a sharp image will be produced on the screen.$d_T$>4$f$
(b) If $d_{\mathrm{T}}>4f,$ show that there will be no lens position where a sharp image is formed.
(c) Determine a formula for the distance between the two lens positions in part (a), and the ratio of the image sizes.

  In a slide or movie projector, mu,x sdxf w;*;yw8+n ithe film acts as the object whose image is projected on a screen (Fig. Below). If a 105-mm-focal-length lens is to project an image on a screen 8.00 m away, howw+ m ,xwny 8;*s;fuixd far from the lens should the slide be? If the slide is 36 mm wide, how wide will the picture be on the screen? $d_0$ =    m $|h_1|$ =    m

  A 35-mm slide (picture size isva8oc5 70r;qq86hf(fy;-pw rmvv gt dfn b7b7 actually 24 by 36 mm) is to be projected on a screen 1.80 m by 2.70 m placed 7.50 m from the projector. What focal-length lens should be used if the image is tf7r7yba rmdhcg ;f86qo5pt-0( vv vwqb;f8n 7o cover the screen?    cm

Show analytically that the image formed by a con*vryq3;; clp6h56;r a bfoq esverging lens is real and inverted if the object is beyond the foc6*y5r;3pslec rv; hq q6a;o fbal point $(d_0>f),$ and is virtual and upright if the object is within the focal point $(d_0>f),$ Describe the image if the object is itself an image, formed by another lens, so its position is beyond the lens, for which $-d_0>f$, and for which $0$<$-d_0$<$f$.

  A movie star catches a reporter shooting picturvcfxbgb f6e1t b/;) f)es of her at home. She claims the reporter was trespassing. To prove her point, she gives as evidence the film she seized. Her 1.75-m height is 8.25 mm high on the film, and the focal length of xc v/gb1 )ebfbf;t)f6 the camera lens was 210 mm. How far away from the subject was the reporter standing?    m

  How large is the image of the Sun on film used in a camera with)bev,k 6d ar)h em+tv2
(a) a 28-mm-focal-length lens,    mm
(b) a 50-mm-focal-length lens,    mm
(c) a 135-mm-focal-length lens?    mm
(d) If the 50-mm lens is considered normal for this camera, what relative magnification does each of the other two lenses provide? The Sun has diameter $1.4\times10^6\mathrm{~km},$ and it is $1.5\times10^8\mathrm{~km}$ away.    for the 28 mm lens    for the 135 mm lens.